In this section, we use a Lorenz-96 model that was first introduced in [1]} to test the performance of the sparse UKF. Consder
\(\begin{array}{lllllllll}\begin{aligned}\displaystyle \frac{dx_i}{dt}&=(x_{i+1}-x_{i-2})x_{i-1}-x_i+F, & i=1, 2, \cdots , n,\\x_{n+1}&=x_1,\\n&=40,\\\Delta t&=0.025,\\F&= 8.\end{aligned}\end{array}\) 
